During the heat treatment process, people use clay to harden the steel in certain areas like the spine. Then they have to go through another process to make the steel tough. I need very hard steel and want to know will the hard steel be brittle and able to withstand large amounts of pressure? I ask because the steel is heavily stressed from the forging process. Also, can I make a thinner piece of steel as hard as a thicker piece with this method?
It depends what you want to achieve and what you mean by 'strength'. .
Heat treating can be used to increase the yield stress of a hardenable steel (to a greater or lesser extent depending on the alloy and process used). But what it won't do is to increase the stiffness of the part as hardening and tempering have no significant effect on the Young's Modulus of steel.
So heat treating will increase the stress at which a part will fail but it won't change how it deflects under load. In the case of a simple beam under bending load it will bend further before it fails but will still bend the same amount under the same load.
If you want to increase the stiffness and reduce weight you need to change the section for example a hollow tube will be much stiffer in bending than a solid one of the same mass per unit length and the same goes for 'I' sections. In other loading conditions webs, ribs and swages can be used to increase stiffness significantly.
In terms of material properties there is usually a trade-off between hardness and toughness (ie the ability to tolerate impact loading) and in some cases it is desirable to sacrifice a bit of hardness and ultimate tensile strength for the sake of ductility in order to prevent brittle failures which tend to be sudden and catastrophic.
In steel hardness is closely related to tensile strength so a hardened steel will have both high hardness and high tensile strength.
Toughness is a bit more difficult to quantify than strength but in general is the ability to resist impact and resistance to brittle fractures. Ductility plays a part in toughness as it tends to help a material to resist crack propagation.
For simple steels heat treating is usually a balance between hardness and toughness. Cooling a hardenable steel from critical temperature (around 850 C) creates a very hard but brittle material, tempering (heating to a lower temperature, around 200-300 C) partially reverses the hardening process and improves toughness and ductility. Controlling the tempering temperature allows the relative hardness/toughness to be controlled to an extent.
The exact properties you get from a given heat treating process will depend on the alloy used and different alloys will have different heat treating requirements.
Prior to hardening residual manufacturing stresses and grain growth can be mitigated by annealing and/or normalising if necessary.
Having said that heat treating steel is a complex subject on which many large and complex books have been written and it's not easy to summarise in a short answer. It is also important that you read up on the precise engineering definitions of the terms involved eg hardness, toughness, tensile strength, ductility etc as they have very specific meanings in this context and talking about 'strength' generally can cause confusion.